SOLUTION: FIND THE PRODUCT. (3x + 5y)^2 Please explain each step. Thank you!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: FIND THE PRODUCT. (3x + 5y)^2 Please explain each step. Thank you!      Log On


   

Question 611060: FIND THE PRODUCT.
(3x + 5y)^2
Please explain each step. Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%283x%2B5y%29%5E2 Start with the given expression.


%283x%2B5y%29%283x%2B5y%29 Expand. Remember something like x%5E2=x%2Ax.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


%28highlight%283x%29%2B5y%29%28highlight%283x%29%2B5y%29 Multiply the First terms:%283%2Ax%29%2A%283%2Ax%29=9%2Ax%5E2.


%28highlight%283x%29%2B5y%29%283x%2Bhighlight%285y%29%29 Multiply the Outer terms:%283%2Ax%29%2A%285%2Ay%29=15%2Ay%2Ax.


%283x%2Bhighlight%285y%29%29%28highlight%283x%29%2B5y%29 Multiply the Inner terms:%285%2Ay%29%2A%283%2Ax%29=15%2Ay%2Ax.


%283x%2Bhighlight%285y%29%29%283x%2Bhighlight%285y%29%29 Multiply the Last terms:%285%2Ay%29%2A%285%2Ay%29=25%2Ay%5E2.


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So we have the terms: 9%2Ax%5E2, 15%2Ay%2Ax, 15%2Ay%2Ax, 25%2Ay%5E2


9%2Ax%5E2%2B15%2Ay%2Ax%2B15%2Ay%2Ax%2B25%2Ay%5E2 Now add every term listed above to make a single expression.


9x%5E2%2B30yx%2B25y%5E2 Now combine like terms.


So %283x%2B5y%29%5E2 FOILs to 9x%5E2%2B30yx%2B25y%5E2.


In other words, %283x%2B5y%29%5E2=9x%5E2%2B30yx%2B25y%5E2 for all values of x and y.

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